Unilateral climate policy induces carbon leakage through the relocation of emission-intensive and trade-exposed industries to regions with no or more lenient emission regulation. Both analytical and numerical studies suggest that emission pricing combined with border carbon adjustments may be a second-best instrument, and more cost-effective than output-based rebating, in which case domestic output is indirectly subsidized. No countries have so far imposed border carbon adjustments, while variants of output-based rebating have been implemented. In this paper we demonstrate that it is welfare improving for a region who has already implemented emission pricing along with output-based rebating for emission-intensive and trade-exposed goods to also introduce a consumption tax on these goods. Moreover, we show that combining output-based rebating with a consumption tax can be equivalent with border carbon adjustments.